I'll preface this with I know it kind of contradicts what I said above but only to a point (y'all got me reading a lot more into this). The initial motivation between an update vs clean-sheet wasn't cost, it was competition, but at the end it was still a series of decisions driven by money not sound engineering or safety. The 737 wasn't supposed to be updated. I won't say never but the actual plan in 2006 was to replace the aircraft with a clean-sheet design following the 787. They kept putting off deciding on the new design until in mid-2010 they committed to making a decision in 2011. Enter Airbus in December 2010 announcing the A320neo program and securing an order of hundreds of planes from the then Boeing dominated American Airlines fleet. The downside for Airbus was that the contract with American hindered their ability to make deal with other airlines, giving Boeing time to react. Boeing pushes off the new airplane to 2030 and rushes to build a more efficient 737 to secure their dominance with other airlines. "Easiest" way to increase efficiency? Larger engines with higher bypass ratios (they also made some aero/weight changes but that's the big one).
The problem is the original 737 was designed with thin turbojets, not turbofans, and also designed to sit as low as possible for weight and maintenance. The new engines don't fit under the wing so they moved them forward, up, and I think slightly in as well. This put them more forward of the lateral axis, increasing moment. Not only that, the engine nacelles themselves now generated a fair bit more lift. This came to a head when doing high speed stall testing where the aircraft would perform relatively as expected but the stick wouldn't The forces on the stick would suddenly drop off through the stall due to the increased lift on the nacelles. FAA cert requirements say that the forces on the stick have to make smooth changes. So while the aircraft was still safe to fly, it didn't meet cert requirements. Enter MCAS. The first iteration used the AoA sensor and a g-input to determine if the aircraft was entering a high speed stall and adjusted the elevator by up to 0.6 degrees to compensate. Test pilots say it works beautifully and the program continues.
Some more test flights and the same stick load issue is discovered during low speed stalls as well. Lower airspeed means larger deflections are required to control the aircraft, and their won't be excessive g-forces to trigger the MCAS system. So Boeing scraps the g-force input, ups the amount of authority of the MCAS system, and allows in to activate multiple successive times in a row stacking the pitch change. Note that while they scrapped the g-input and the 737 has two AoA sensors, they never update it to read more than one. Test pilots, engineers, designers all raise concerns but are shouted down and literally told "Don't rock the boat." The safety assessment relies on the pilots assessing and correcting a runaway pitch condition within 3 seconds, which was never going to happen for several reasons.
The accidents that happened were caused when that single AoA sensor failed and the MCAS system activated. A pilot may recognize a single specific issue in 3 seconds but that's not the cockpit environment when an AoA sensor fails. Master warning, stall warning, stick shaker, TAWS, overspeed, wildly spinning trim wheel, and who knows what else all suddenly comes on at the same time. The pilot figures out that nose is pitching down and yanks the yoke. Too bad the force required to pull up is suddenly well over 40 or 50 pounds. The pilot recognizes the runaway elevator and does the standard procedure of hitting the trim switch to correct. Too bad the MCAS system disables the yoke trim switch when it's activated. Go to the flight manual for the runaway elevator procedure to see what to do about MCAS. Except there's nothing in there about it. Boeing made an extremely conscious decision to leave it out. Transition training from the older 737s to the max? Nothing about MCAS was there either.
So in the aftermath people turn to Boeing for answers. Why wasn't it designed safer? Why was the system reliant on a single input? Why weren't the pilots trained? Boeing's response: We did everything right. The system passed the legal requirements, our system safety assessment showed it was safe per the requirements, and the training provided was more than enough for the pilots. One hour on an iPad. You want to know why those planes crashed? Ask the pilots flying them. (This response was disgusting then and more so now with this next part coming to light).
People probe deeper and the truth comes out. MCAS was a band-aid. It was tested in its original form but not in it's second evolution. Why? Because management actively suppressed flight testing of it. A new system safety report wasn't written for the new system. Why? They did a back of the envelope calculation and figured they didn't have to. The flight manual didn't continue info about MCAS or how to disable it. Why? Boeing worked very hard to convince the FAA that they didn't need it. They didn't want people to be aware of how different the aircraft really was (various reasons for that, but it all comes back to money). There was no real training program for the transition pilots. Why? Same as above.
So where are we now? The FAA is auditing everything Boeing has, likely finding more issues. That'll happen, there's an absolutely insane amount of documentation, mistakes are going to happen, mostly innocent ones. Boeing is losing huge amounts of money due to the grounding and lost faith in their safety. Customers losing faith in Boeing products, but this is absolutely true:
Boeing continues to insist they bear no fault and people shouldn't stop trusting them. And 346 people are dead. Gone. Never to be seen again. All because Boeing couldn't be bothered to change an 'if/then' statement to 'if/if(and)/then/else'.